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komm.FibonacciCode

Fibonacci code. It is an integer code with domain the positive integers. The codeword for an integer $n$ consists of the Zeckendorf representation of $n$ (a sum of non-consecutive Fibonacci numbers $1, 2, 3, 5, 8, \ldots$), least significant bit first, followed by an extra $1$. For more details, see Wikipedia: Fibonacci coding.

The table below shows the codewords for the first integers, with a space between the two parts.

$n$ Codeword
$1$ 1 1
$2$ 01 1
$3$ 001 1
$4$ 101 1
$5$ 0001 1
$6$ 1001 1
$7$ 0101 1
$8$ 00001 1

encode_single()

Encodes a single integer into its codeword.

Parameters:

  • integer (SupportsIndex) –

    The integer to be encoded. Must be in the domain of the code.

Returns:

  • codeword (Word) –

    The codeword of the integer. It is a tuple of bits.

Examples:

>>> code = komm.FibonacciCode()
>>> code.encode_single(4)
(1, 0, 1, 1)

decode_single()

Decodes a single codeword from a bit iterator. This method consumes exactly the bits of one codeword, leaving the iterator at the boundary with the next one; any remaining bits are left untouched.

Parameters:

  • bits (Iterator[SupportsIndex]) –

    An iterator of bits starting with a complete codeword. It must be an iterator (as returned by iter), not a general iterable, since advancing it is part of the contract.

Returns:

  • integer (int) –

    The decoded integer.

Notes

A ValueError is raised if the iterator is exhausted mid-codeword or if an invalid bit is found.

Examples:

>>> code = komm.FibonacciCode()
>>> bits = iter([1, 0, 1, 1, 0, 1])
>>> code.decode_single(bits)
4
>>> list(bits)  # Iterator is left at codeword boundary
[0, 1]

length()

Returns the codeword length $\ell(n)$ for a given integer $n$ in the domain of the code.

Examples:

>>> code = komm.FibonacciCode()
>>> code.length(4)
4

encode()

Encodes a sequence of integers.

Parameters:

  • input (ArrayLike) –

    The sequence of integers to be encoded. Must be a 1D-array of positive integers.

Returns:

  • output (Array1D[integer]) –

    The concatenation of the codewords. It is a 1D-array of bits.

Examples:

>>> code = komm.FibonacciCode()
>>> code.encode([4, 1, 3])
array([1, 0, 1, 1, 1, 1, 0, 0, 1, 1])

decode()

Decodes a sequence of bits.

Parameters:

  • input (ArrayLike) –

    The sequence of bits to be decoded. Must be a 1D-array of bits. Also, the sequence must be a concatenation of codewords (i.e., the output of the encode method).

Returns:

  • output (Array1D[integer]) –

    The sequence of decoded integers. It is a 1D-array of positive integers.

Examples:

>>> code = komm.FibonacciCode()
>>> code.decode([1, 0, 1, 1, 1, 1, 0, 0, 1, 1])
array([4, 1, 3])